关于函数曲线的渐近线概念的探讨

Discussion on Asymptote Concepts of Curvilinear Functions

现今一些高等数学教科书中关于渐近线的讨论比较含糊,存在欠缺,主要表现在:一是按照其渐近线的概念进行讨论,将会丢失一些渐近线。二是讨论渐近线是为了帮助分析函数曲线的走向,而其提出的渐近线概念对此帮助不大。为此,提出了关于完善渐近线概念的思考,并对曲线与其渐近线的几何位置关系进行了比较明确的探讨,基本上解决了上述两点不足。

Two critical flaws concerning ambiguities for asymptotes are existed in advanced mathematics textbook today ： （ 1 ） if the discussion is determined by the asymptote concepts ,a few particular asymptotes can be lost; （2） since the discussion on as- ymptotes is used to analyze the trend of the function curve, the asymptote concept gives little support to the discussion. This paper gives a new concept about asymptote - perfecting . The geometrical relation with the asymptote are discussed, thus solving those two problems.